Evolution of convex lens-shaped networks under the curve shortening flow

No Thumbnail Available
Files
There are no files associated with this item.
Date
2011
Authors
Azouani, Abderrahim
Georgi, Marc
Hell, Juliette
Jangle, Nihar
Koeller, Amos
Marxen, Tobias
Ritthaler, Sandra
Sáez, Mariel
Schulze, Felix
Editors
Contact
Journal ISSN
Electronic ISSN
ISBN
Bibliographical data
Publisher
Series
URI (citable link)
DOI (citable link)
ArXiv-ID
International patent number
Link to the license
EU project number
Project
Open Access publication
Restricted until
Title in another language
Research Projects
Organizational Units
Journal Issue
Publication type
Journal article
Publication status
Published in
Transactions of the American Mathematical Society ; 363 (2011), 5. - pp. 2265-2294
Abstract
We consider convex symmetric lens-shaped networks in R2 that evolve under the curve shortening flow. We show that the enclosed convex domain shrinks to a point in finite time. Furthermore, after appropriate rescaling the evolving networks converge to a self-similarly shrinking network, which we prove to be unique in an appropriate class. We also include a classification result for some self-similarly shrinking networks.
Summary in another language
Subject (DDC)
510 Mathematics
Keywords
Conference
Review
undefined / . - undefined, undefined. - (undefined; undefined)
Cite This
ISO 690SCHNÜRER, Oliver C., Abderrahim AZOUANI, Marc GEORGI, Juliette HELL, Nihar JANGLE, Amos KOELLER, Tobias MARXEN, Sandra RITTHALER, Mariel SÁEZ, Felix SCHULZE, Brian SMITH, 2011. Evolution of convex lens-shaped networks under the curve shortening flow. In: Transactions of the American Mathematical Society. 363(5), pp. 2265-2294
BibTex
@article{Schnurer2011Evolu-19149,
  year={2011},
  title={Evolution of convex lens-shaped networks under the curve shortening flow},
  number={5},
  volume={363},
  journal={Transactions of the American Mathematical Society},
  pages={2265--2294},
  author={Schnürer, Oliver C. and Azouani, Abderrahim and Georgi, Marc and Hell, Juliette and Jangle, Nihar and Koeller, Amos and Marxen, Tobias and Ritthaler, Sandra and Sáez, Mariel and Schulze, Felix and Smith, Brian}
}
RDF
<rdf:RDF
    xmlns:dcterms="http://purl.org/dc/terms/"
    xmlns:dc="http://purl.org/dc/elements/1.1/"
    xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
    xmlns:bibo="http://purl.org/ontology/bibo/"
    xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
    xmlns:foaf="http://xmlns.com/foaf/0.1/"
    xmlns:void="http://rdfs.org/ns/void#"
    xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > 
  <rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/19149">
    <dc:creator>Jangle, Nihar</dc:creator>
    <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
    <dc:creator>Sáez, Mariel</dc:creator>
    <dcterms:rights rdf:resource="https://rightsstatements.org/page/InC/1.0/"/>
    <dc:creator>Koeller, Amos</dc:creator>
    <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2012-05-02T09:50:57Z</dc:date>
    <dc:creator>Schulze, Felix</dc:creator>
    <dc:contributor>Sáez, Mariel</dc:contributor>
    <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2012-05-02T09:50:57Z</dcterms:available>
    <dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:contributor>Georgi, Marc</dc:contributor>
    <dc:contributor>Jangle, Nihar</dc:contributor>
    <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/19149"/>
    <dc:creator>Schnürer, Oliver C.</dc:creator>
    <dc:creator>Marxen, Tobias</dc:creator>
    <dc:creator>Hell, Juliette</dc:creator>
    <dc:contributor>Schnürer, Oliver C.</dc:contributor>
    <dcterms:abstract xml:lang="eng">We consider convex symmetric lens-shaped networks in R2 that evolve under the curve shortening flow. We show that the enclosed convex domain shrinks to a point in finite time. Furthermore, after appropriate rescaling the evolving networks converge to a self-similarly shrinking network, which we prove to be unique in an appropriate class. We also include a classification result for some self-similarly shrinking networks.</dcterms:abstract>
    <dc:contributor>Koeller, Amos</dc:contributor>
    <dc:contributor>Ritthaler, Sandra</dc:contributor>
    <dcterms:issued>2011</dcterms:issued>
    <dc:contributor>Azouani, Abderrahim</dc:contributor>
    <dc:contributor>Schulze, Felix</dc:contributor>
    <dc:rights>terms-of-use</dc:rights>
    <dc:language>eng</dc:language>
    <dc:creator>Ritthaler, Sandra</dc:creator>
    <foaf:homepage rdf:resource="http://localhost:8080/"/>
    <dcterms:bibliographicCitation>Publ. in: Transactions of the American Mathematical Society ; 363 (2011), 5. - pp. 2265-2294</dcterms:bibliographicCitation>
    <dc:contributor>Marxen, Tobias</dc:contributor>
    <dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
    <dc:creator>Smith, Brian</dc:creator>
    <dc:contributor>Hell, Juliette</dc:contributor>
    <dcterms:title>Evolution of convex lens-shaped networks under the curve shortening flow</dcterms:title>
    <dc:creator>Georgi, Marc</dc:creator>
    <dc:creator>Azouani, Abderrahim</dc:creator>
    <dc:contributor>Smith, Brian</dc:contributor>
  </rdf:Description>
</rdf:RDF>
Internal note
xmlui.Submission.submit.DescribeStep.inputForms.label.kops_note_fromSubmitter
Contact
URL of original publication
Test date of URL
Examination date of dissertation
Method of financing
Comment on publication
Alliance license
Corresponding Authors der Uni Konstanz vorhanden
International Co-Authors
Bibliography of Konstanz
Yes
Refereed